Lithium secondary batteries have high energy density and good cycle performance. Accordingly, recently, these have been rapidly used as small-sized batteries for a power supply for portable devices or the like. On the other hand, development for large-sized batteries for the electric power industry, automobiles and the like has been demanded. These large-sized lithium secondary batteries need to comprise an electrode active material having long-term reliability and high input and output properties. Particularly, for the negative electrode active material, lithium titanate having high security, long life, and excellent rate property has been expected, and a variety of lithium titanate has been proposed for the electrode active material. For example, a lithium titanate is known which is granulated into spherical secondary particles to improve packing properties, and thereby to improve battery properties (Patent Documents 1 and 2). Such lithium titanate secondary particles are produced by granulating with drying a titanium compound and a lithium compound, and firing the granulated product. Further, in order to improve the discharge capacity of the lithium titanate secondary particles, a process in which a slurry comprising crystalline titanium oxide, a titanic acid compound, and a lithium compound is granulated with drying, and then the granulated product is heated and fired employs a process such as a process of preparing the slurry by adding a crystalline titanium oxide and a titanic acid compound to a solution of a lithium compound preheated to 50° C. or more (Patent Document 3), or a process of preparing the slurry at a temperature of less than 45° C. (Patent Document 4). On the other hand, a technique is known in which lithium titanate is crushed and fired again to form pores having an average pore size in the range of 50 to 500 Å on the surface of the particle of lithium titanate, thereby improving high current properties and cycle performance (Patent Document 5).